Aliasing-tolerant sub-Nyquist sampling of FRI signals

Abstract

This paper addresses the sampling of Finite Rate of Innovation (FRI) signals and proposes new lower bounds for accurate reconstruction. Recently, the FRI approach has been established next to the Compressed Sensing framework to deal with signals which are sparse in their parametric description. Many authors showed that a reconstruction is exactly possible in the absence of noise and, therefore, lower bounds on the sampling rate have been presented. Furthermore, different sampling kernels have been proposed such as the Sum of Sinc (SoS) kernel or the Gaussian low pass kernel. This contribution is motivated by a practical system design for sampling FRI signals with a fixed SoS filter design but varying Rate of Innovation (RoI). Therefore, a varying sampling rate is desired as well. For the proposed system design sampling below the previously presented bounds, i.e. below twice the kernel bandwidth, is analysed. This means sampling is applied in a sub-Nyquist regime with respect to the sampling kernel. The aliasing effect is analysed and new bounds are presented which allow a stable reconstruction. This analysis is supported by numerical simulation.